
import numpy as np
import pandas as pd
import biocircuits 
import scipy.integrate
import scipy.signal

import bokeh.io
bokeh.io.output_notebook()
import panel as pn
pn.extension()

def style(p, autohide=False):
    p.title.text_font="Helvetica"
    p.title.text_font_size="16px"
    p.title.align="center"
    p.xaxis.axis_label_text_font="Helvetica"
    p.yaxis.axis_label_text_font="Helvetica"
    
    p.xaxis.axis_label_text_font_size="13px"
    p.yaxis.axis_label_text_font_size="13px"
    p.background_fill_alpha = 0
    if autohide: p.toolbar.autohide=True
    return p


import warnings 
warnings.filterwarnings("ignore") # for those pesky pesky exponents/denominators


beta_x_slider = pn.widgets.FloatSlider(name="βx", start=0.1, end=10.0, step=0.1, value=0.7, width=100)
beta_y_slider = pn.widgets.FloatSlider(name="βy", start=0.1, end=10.0, step=0.1, value=0.7, width=100)
gamma_slider = pn.widgets.FloatSlider(name="γ", start=0.1, end=10.0, step=0.1, value=1.0, width=100)
k1_slider = pn.widgets.FloatSlider(name="κ1", start=0.01, end=3, step=0.1, value=1.5, width=100)
k2_slider = pn.widgets.FloatSlider(name="κ2", start=0.01, end=3, step=0.1, value=1.5, width=100)
n_xx_slider = pn.widgets.FloatSlider(name="n_xx", start=5, end=15.0, step=0.1, value=7, width=100)
n_xy_slider = pn.widgets.FloatSlider(name="n_xy", start=5, end=15.0, step=0.1, value=7, width=100)
n_yy_slider = pn.widgets.FloatSlider(name="n_yy", start=5, end=15.0, step=0.1, value=7, width=100)
n_yx_slider = pn.widgets.FloatSlider(name="n_yx", start=5, end=15.0, step=0.1, value=7, width=100)

x_range_slider = pn.widgets.RangeSlider(name="x-range", start=0, end=5, step=0.1, value=(0.2, 0.8), width=300)
y_range_slider = pn.widgets.RangeSlider(name="y-range", start=0, end=5, step=0.1, value=(0.2, 0.8), width=300)
@pn.depends(beta_x_slider.param.value, beta_y_slider.param.value, gamma_slider.param.value, 
            k1_slider.param.value, k2_slider.param.value, 
            n_xx_slider.param.value, n_xy_slider.param.value, 
            n_yy_slider.param.value, n_yx_slider.param.value, 
            x_range_slider.param.value, y_range_slider.param.value
           )

def plotter(beta_x, beta_y, gamma, k1, k2, n_xx, n_xy, n_yy, n_yx, x_range, y_range):
    nx, ny = 500, 500
    x_min, x_max = x_range
    y_min, y_max = y_range

    x = np.linspace(x_min, x_max, nx)
    y = np.linspace(y_min, y_max, ny)
    
    # ............ STREAMPLOT ............ 
    xx, yy = np.meshgrid(x, y, indexing="ij")

    u = np.empty((nx, ny))
    v = np.empty((nx, ny))
    
    for i in range(nx):
        for j in range(ny):
            _x, _y = xx[i, j], yy[i, j]

            num = 1 + _x**n_xx + _x**n_xx*(k1*_y)**n_yx
            denom = (1+_x**n_xx) * (1+(k1*_y)**n_yx)
            u[i, j] = beta_x * num/denom - _x

            num = 1 + _y**n_yy + _y**n_yy*(k2*_x)**n_xy
            denom = (1+_y**n_yy) * (1+(k2*_x)**n_xy)
            v[i, j] = beta_y * num/denom - gamma * _y

    p = bokeh.plotting.figure(
            height=600, width=600, 
            title=(f"βx:{np.round(beta_x,2)}   βy:{np.round(beta_y,2)}   " +
                    f"γ:{np.round(gamma, 2)}   κ1: {np.round(k1, 2)}   " +
                    f"κ2: {np.round(k2, 2)}"))
    p = biocircuits.streamplot(x, y, u, v, p=p, density=3.5, color="#74A0B2")

    nx, ny = 100000, 100000
    x = np.linspace(x_min, x_max+10, nx)
    y = np.linspace(y_min, y_max+10, ny)
    # ............ NULLCLINES ............ 
    _x = 1/k2 * ((beta_y/gamma) / (y**(n_yy+1)-(beta_y/gamma)*(y**n_yy)+y) - 1)**(1/n_xy) 
    _y = 1/k1 * ((beta_x)/(x**(n_xx+1)-beta_x*(x**n_xx)+x) -1 )**(1/n_yx)

    p.line(x, _y, line_color="#1c2641", line_width=1.5)
    p.line(_x, y, line_color="#1c2641", line_width=1.5)
    return style(p)


lay_widgets = pn.Row(pn.Column(beta_x_slider, beta_y_slider), 
                     pn.Column(k1_slider, k2_slider), 
                     pn.Column(n_xx_slider, n_xy_slider),
                     pn.Column(n_yx_slider, n_yy_slider),
                     pn.Column(gamma_slider, align="center"),
                    )
lay_range = pn.Column(x_range_slider, y_range_slider, align="center")
pn.Column(lay_widgets, plotter, lay_range)